Starting Out - Continued...

Is it dangerous?

No. The rules of fencing put safety foremost, and given the proper protective clothing, injuries from blades are very rare. Although it is possible for a blade to break and leave a sharp end (they are tempered so that if they do break they normally do so squarely), the jacket will normally still stop or slow the blade sufficiently to avoid a deep wound. As far as I am aware, in the last 50 years there have been more deaths during competitive golf than there has been in competitive fencing - an impressive record considering its heritage and nature.
 A more likely injury is a muscle tear or sprain - fencing does require you to change direction and move quickly. Properly warming up prior to starting to fence makes this another rare occurrence, though.

Does it take long to become a good fencer?

Yes. And there is a high drop-out rate amongst new fencers for this reason. Fencing involves a lot of movements that do not come naturally, and it takes a good while to become even vaguely proficient. However, those who stick with it tend to keep fencing for a very long time, and as they get older can make up in skill and experience what they lose in speed and agility. But there is always something new to learn.
As with most sports, it's better to start young. Obviously the individual must be physically capable of handling the weapon and mature enough to do so safely (waving swords at unmasked fencers is a good way to find yourself out on your ear), but most clubs allow fencers to start at around eight to ten years of age.